%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN556-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:17:50 AM UTC 2026
% Result : Unsatisfiable 7.32s 2.33s
% Output : Refutation 7.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 12
% Syntax : Number of formulae : 108 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 314 ( 65 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1476 ( 140 ~; 116 |; 0 &;1220 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 163 ( 0 ^; 163 !; 0 ?; 163 :)
% Comments :
%------------------------------------------------------------------------------
thf(p2_decl,type,
p2: $i > $i > $o ).
thf(p3_decl,type,
p3: $i > $i > $o ).
thf(c10_decl,type,
c10: $i ).
thf(c13_decl,type,
c13: $i ).
thf(f7_decl,type,
f7: $i > $i ).
thf(f6_decl,type,
f6: $i > $i ).
thf(c9_decl,type,
c9: $i ).
thf(f4_decl,type,
f4: $i > $i > $i > $i ).
thf(f5_decl,type,
f5: $i > $i > $i ).
thf(f8_decl,type,
f8: $i > $i > $i ).
thf(c11_decl,type,
c11: $i ).
thf(c12_decl,type,
c12: $i ).
thf(3,negated_conjecture,
c13 @ ( c10 @ p2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_3) ).
thf(21,plain,
c13 @ ( c10 @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_4) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( ( c13 @ ( c10 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[21,25]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( ( c13 @ ( c10 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(46,plain,
c13 @ f7 @ ( c10 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( c10 )),bind(B,$thf( c13 ))]]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ ( c10 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[46,25]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ ( c10 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(53,plain,
c13 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( c10 @ f7 )),bind(B,$thf( c13 @ f7 ))]]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[53,25]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(101,plain,
c13 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( c10 @ f7 @ f7 )),bind(B,$thf( c13 @ f7 @ f7 ))]]) ).
thf(10,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p2 ) )
| ~ ( C @ ( A @ p2 ) )
| ( D @ ( C @ f5 ) @ ( B @ ( A @ f5 ) @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_10) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p2 ) )
| ~ ( C @ ( A @ p2 ) )
| ( D @ ( C @ f5 ) @ ( B @ ( A @ f5 ) @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[101,25]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(112,plain,
c13 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( c10 @ f7 @ f7 @ f7 )),bind(B,$thf( c13 @ f7 @ f7 @ f7 ))]]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[112,25]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(123,plain,
c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( c10 @ f7 @ f7 @ f7 @ f7 )),bind(B,$thf( c13 @ f7 @ f7 @ f7 @ f7 ))]]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[123,25]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(134,plain,
c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( c10 @ f7 @ f7 @ f7 @ f7 @ f7 )),bind(B,$thf( c13 @ f7 @ f7 @ f7 @ f7 @ f7 ))]]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[134,25]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(149,plain,
c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[148:[bind(A,$thf( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 )),bind(B,$thf( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 ))]]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[149,25]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(189,plain,
c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 )),bind(B,$thf( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 ))]]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[189,25]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(200,plain,
c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 )),bind(B,$thf( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 ))]]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[200,25]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 )),bind(B,$thf( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 ))]]) ).
thf(5,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_5) ).
thf(13,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(378,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ ( c10 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[46,28]) ).
thf(379,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ ( c10 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
inference(simp,[status(thm)],[378]) ).
thf(380,plain,
c13 @ f7 @ f6 @ ( c10 @ f7 @ f6 @ p2 ),
inference(pattern_uni,[status(thm)],[379:[bind(A,$thf( c10 @ f7 )),bind(B,$thf( c13 @ f7 ))]]) ).
thf(8,negated_conjecture,
c11 @ ( c12 @ f7 @ f6 @ ( c13 @ ( c11 @ f8 ) @ f5 ) @ ( c13 @ f4 ) ) @ ( c9 @ p3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_8) ).
thf(23,plain,
c11 @ ( c12 @ f7 @ f6 @ ( c13 @ ( c11 @ f8 ) @ f5 ) @ ( c13 @ f4 ) ) @ ( c9 @ p3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,negated_conjecture,
~ ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( c9 @ p3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p3_9) ).
thf(17,plain,
~ ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( c9 @ p3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
~ ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( c9 @ p3 ) ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(35,plain,
( ( ( c11 @ ( c12 @ f7 @ f6 @ ( c13 @ ( c11 @ f8 ) @ f5 ) @ ( c13 @ f4 ) ) @ ( c9 @ p3 ) )
!= ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( c9 @ p3 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,29]) ).
thf(36,plain,
( ( c11 @ ( c12 @ f7 @ f6 @ ( c13 @ ( c11 @ f8 ) @ f5 ) @ ( c13 @ f4 ) ) @ ( c9 @ p3 ) )
!= ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( c9 @ p3 ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(38,plain,
( ( ( c11 @ ( c12 @ f7 @ f6 @ ( c13 @ ( c11 @ f8 ) @ f5 ) @ ( c13 @ f4 ) ) )
!= ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) ) )
| ( c9 != c9 ) ),
inference(simp,[status(thm)],[36]) ).
thf(40,plain,
( ( c11 @ ( c12 @ f7 @ f6 @ ( c13 @ ( c11 @ f8 ) @ f5 ) @ ( c13 @ f4 ) ) )
!= ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(143,plain,
( ( c11 != c11 )
| ( ( c12 @ f7 @ f6 @ ( c13 @ ( c11 @ f8 ) @ f5 ) )
!= ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) ) )
| ( c13 != c10 ) ),
inference(simp,[status(thm)],[40]) ).
thf(144,plain,
( ( ( c12 @ f7 @ f6 @ ( c13 @ ( c11 @ f8 ) @ f5 ) )
!= ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) ) )
| ( c13 != c10 ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
( ( ( c12 @ f7 @ f6 )
!= ( c12 @ f7 @ f6 ) )
| ( ( c13 @ ( c11 @ f8 ) )
!= ( c10 @ ( c11 @ f8 ) ) )
| ( c13 != c10 ) ),
inference(simp,[status(thm)],[144]) ).
thf(146,plain,
( ( ( c13 @ ( c11 @ f8 ) )
!= ( c10 @ ( c11 @ f8 ) ) )
| ( c13 != c10 ) ),
inference(simp,[status(thm)],[145]) ).
thf(158,plain,
( ( c13 != c10 )
| ( c11 != c11 )
| ( c13 != c10 ) ),
inference(simp,[status(thm)],[146]) ).
thf(159,plain,
c13 != c10,
inference(simp,[status(thm)],[158]) ).
thf(2,negated_conjecture,
! [A: $i] : ( A @ ( A @ p3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_2) ).
thf(18,plain,
! [A: $i] : ( A @ ( A @ p3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( ( c13 @ ( c10 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[21,28]) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( ( c13 @ ( c10 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(386,plain,
c13 @ f6 @ ( c10 @ f6 @ p2 ),
inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( c10 )),bind(B,$thf( c13 ))]]) ).
thf(12,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ p2 ) )
| ~ ( F @ ( C @ p3 ) )
| ~ ( E @ ( B @ p2 ) )
| ( F @ ( E @ ( D @ f4 ) ) @ ( C @ ( B @ ( A @ f4 ) ) @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_12) ).
thf(19,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ p2 ) )
| ~ ( F @ ( C @ p3 ) )
| ~ ( E @ ( B @ p2 ) )
| ( F @ ( E @ ( D @ f4 ) ) @ ( C @ ( B @ ( A @ f4 ) ) @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_7) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ p3 ) )
!= ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( c9 @ p3 ) ) )
| ~ $true
| ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,29]) ).
thf(173,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ p3 ) )
!= ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( c9 @ p3 ) ) )
| ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(174,plain,
! [A: $i] :
( ~ ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( A @ p3 ) )
| ~ ( c9 @ ( A @ p3 ) ) ),
inference(pattern_uni,[status(thm)],[173:[bind(A,$thf( c9 )),bind(B,$thf( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) )),bind(C,$thf( C ))]]) ).
thf(186,plain,
! [A: $i] :
( ~ ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( A @ p3 ) )
| ~ ( c9 @ ( A @ p3 ) ) ),
inference(simp,[status(thm)],[174]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ p3 ) )
!= ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( B @ p3 ) ) )
| ~ $true
| ~ ( c9 @ ( B @ p3 ) ) ),
inference(paramod_ordered,[status(thm)],[18,186]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ p3 ) )
!= ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( B @ p3 ) ) )
| ~ ( c9 @ ( B @ p3 ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(242,plain,
~ ( c9 @ ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) )),bind(B,$thf( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) ))]]) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[211,25]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[220]) ).
thf(222,plain,
c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[221:[bind(A,$thf( c10 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 )),bind(B,$thf( c13 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 @ f7 ))]]) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( B @ ( C @ p3 ) )
!= ( A @ ( C @ p3 ) ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
inference(eqfactor_ordered,[status(thm)],[27]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p3 ) )
| ( A @ ( A @ p3 ) ) ),
inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( B ))]]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p3 ) )
| ( A @ ( A @ p3 ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(414,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f6 @ ( c10 @ f6 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[386,25]) ).
thf(415,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f6 @ ( c10 @ f6 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[414]) ).
thf(416,plain,
c13 @ f6 @ f7 @ ( c10 @ f6 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[415:[bind(A,$thf( c10 @ f6 )),bind(B,$thf( c13 @ f6 ))]]) ).
thf(428,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f6 @ ( c10 @ f7 @ f6 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[380,25]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f6 @ ( c10 @ f7 @ f6 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f7 @ ( A @ f7 @ p2 ) ) ),
inference(simp,[status(thm)],[428]) ).
thf(430,plain,
c13 @ f7 @ f6 @ f7 @ ( c10 @ f7 @ f6 @ f7 @ p2 ),
inference(pattern_uni,[status(thm)],[429:[bind(A,$thf( c10 @ f7 @ f6 )),bind(B,$thf( c13 @ f7 @ f6 ))]]) ).
thf(11,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ p3 ) )
| ~ ( D @ ( B @ p2 ) )
| ( D @ ( C @ f8 ) @ ( B @ ( A @ f8 ) @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_11) ).
thf(22,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ p3 ) )
| ~ ( D @ ( B @ p2 ) )
| ( D @ ( C @ f8 ) @ ( B @ ( A @ f8 ) @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f6 @ ( c10 @ f6 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[386,28]) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f6 @ ( c10 @ f6 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
inference(simp,[status(thm)],[417]) ).
thf(419,plain,
c13 @ f6 @ f6 @ ( c10 @ f6 @ f6 @ p2 ),
inference(pattern_uni,[status(thm)],[418:[bind(A,$thf( c10 @ f6 )),bind(B,$thf( c13 @ f6 ))]]) ).
thf(33,plain,
! [A: $i] :
( ( ( A @ ( A @ p3 ) )
!= ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( c9 @ p3 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,29]) ).
thf(34,plain,
! [A: $i] :
( ( A @ ( A @ p3 ) )
!= ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) @ ( c9 @ p3 ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(37,plain,
! [A: $i] :
( ( A
!= ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) ) )
| ( A != c9 ) ),
inference(simp,[status(thm)],[34]) ).
thf(39,plain,
( ( c11 @ ( c12 @ f7 @ f6 @ ( c10 @ ( c11 @ f8 ) @ f5 ) @ ( c10 @ f4 ) ) )
!= c9 ),
inference(simp,[status(thm)],[37]) ).
thf(6,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_6) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(357,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ~ $true
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[53,28]) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( ( c13 @ f7 @ f7 @ ( c10 @ f7 @ f7 @ p2 ) )
!= ( B @ ( A @ p2 ) ) )
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
inference(simp,[status(thm)],[357]) ).
thf(359,plain,
c13 @ f7 @ f7 @ f6 @ ( c10 @ f7 @ f7 @ f6 @ p2 ),
inference(pattern_uni,[status(thm)],[358:[bind(A,$thf( c10 @ f7 @ f7 )),bind(B,$thf( c13 @ f7 @ f7 ))]]) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p2 ) )
| ~ ( C @ ( A @ p2 ) )
| ( D @ ( C @ f5 ) @ ( B @ ( A @ f5 ) @ p2 ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p3 ) )
!= ( C @ ( D @ p3 ) ) )
| ~ $true
| ~ ( B @ ( D @ p3 ) )
| ( C @ ( B @ p3 ) ) ),
inference(paramod_ordered,[status(thm)],[18,27]) ).
thf(170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p3 ) )
!= ( C @ ( D @ p3 ) ) )
| ~ ( B @ ( D @ p3 ) )
| ( C @ ( B @ p3 ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p3 ) )
| ( A @ ( B @ p3 ) ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(1,negated_conjecture,
! [A: $i] : ( A @ ( A @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_1) ).
thf(15,plain,
! [A: $i] : ( A @ ( A @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(645,plain,
$false,
inference(e,[status(thm)],[101,14,211,380,53,13,134,159,18,386,19,242,222,185,24,25,189,20,46,416,29,28,21,430,17,149,22,27,419,39,112,123,16,359,40,26,186,171,23,15,200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN556-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 18:13:37 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.58/0.69 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.79 % [INFO] Parsing done (94ms).
% 0.71/0.80 % [INFO] Running in sequential loop mode.
% 1.16/0.99 % [INFO] eprover registered as external prover.
% 1.16/0.99 % [INFO] Scanning for conjecture ...
% 1.44/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.44/1.08 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.44/1.08 % [INFO] Problem is propositional (TPTP CNF).
% 1.44/1.08 % [INFO] Type checking passed.
% 1.44/1.08 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.32/2.32 % External prover 'e' found a proof!
% 7.32/2.32 % [INFO] Killing All external provers ...
% 7.32/2.32 % Time passed: 1838ms (effective reasoning time: 1524ms)
% 7.32/2.32 % Axioms used in derivation (0):
% 7.32/2.32 % No. of inferences in proof: 108
% 7.32/2.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1838 ms resp. 1524 ms w/o parsing
% 7.32/2.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.32/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------